Bayern, which lost the German League title for the first time in 11 years to Bayer Leverkusen with five rounds to go, will face Manchester City or Real Madrid in the semi-finals.
Kimmich scored the only goal of the match in the 63rd minute after Rafael Guerrero sent a cross pass, which the German international met with a powerful header that went into Arsenal’s net.
Gabriel Martinelli almost scored for the visiting team after 20 minutes when he dribbled past Bayern’s defenders, but Bayern goalkeeper Manuel Neuer quickly left his goal to pounce on the ball before the Brazilian winger.
Moroccan Nassir Mazraoui, Bayern’s player, fired a shot from close range two minutes later, but Arsenal goalkeeper David Raya successfully saved it.
Martinelli returned to waste a clear opportunity after half an hour when he received a cross pass from Martin Odegaard and met it with a shot inside the penalty area, but it easily reached goalkeeper Neuer.
Gamal Musiala almost decided the match with a second goal in the 87th minute when he fired a shot from the left of the penalty area, but goalkeeper Raya successfully saved it.
Odegaard fired a powerful shot from the right of the penalty area, and Neuer appeared to deflect it into a corner kick, but the referee awarded it a goal kick, which angered the Arsenal captain.
Musiala returned to waste another opportunity one minute before the end of regular time when he shot from inside the penalty area, but Raya successfully blocked it.
Arsenal’s performance, which has not reached the semi-finals since 2009, did not change in the final minutes despite coach Mikel Arteitia’s changes by including Gabriel Jesus and Leandro Trossard.
Bayern qualified for the semi-finals for the first time in four years when it won the title in 2020.
